> ## Documentation Index
> Fetch the complete documentation index at: https://docs.fincept.in/llms.txt
> Use this file to discover all available pages before exploring further.

# Black-Scholes Full Greeks Suite

> Calculate complete suite of Black-Scholes Greeks including price and all first-order and second-order risk sensitivities. This is the most comprehensive Greeks calculation endpoint.

**Greeks Calculated:**
- **Price**: Option theoretical value
- **Delta**: Sensitivity to underlying price (∂V/∂S)
- **Gamma**: Sensitivity of delta to underlying price (∂²V/∂S²)
- **Vega**: Sensitivity to volatility (∂V/∂σ)
- **Theta**: Sensitivity to time decay (∂V/∂t)
- **Rho**: Sensitivity to interest rate (∂V/∂r)
- **Vanna**: Cross-sensitivity to spot and volatility (∂²V/∂S∂σ)
- **Volga**: Sensitivity of vega to volatility (∂²V/∂σ²)

**Use Cases:**
- Complete risk management analysis
- Portfolio hedging calculations
- Option trading strategy evaluation
- Greeks-based position monitoring

**Tier:** Standard (2 credits/request) [Tier: PRO, Credits: 5]



## OpenAPI

````yaml api-specs/pricing.json post /quantlib/pricing/bs/greeks-full
openapi: 3.1.0
info:
  title: FinceptQuantLib API - Pricing Module
  description: >-
    Advanced options pricing models including Black-Scholes, Black76, Bachelier,
    Kirk spread options, and binomial trees. Standard Tier access required (2
    credits per request).
  version: 3.0.0
  contact:
    name: Fincept API Support
    url: https://fincept.in
servers:
  - url: https://api.fincept.in
    description: Fincept API Production Server
security:
  - APIKeyHeader: []
tags:
  - name: quantlib-pricing
    description: Advanced options pricing models and Greeks calculation
    x-displayName: Pricing
paths:
  /quantlib/pricing/bs/greeks-full:
    post:
      tags:
        - quantlib-pricing
      summary: Black-Scholes Full Greeks Suite
      description: >-
        Calculate complete suite of Black-Scholes Greeks including price and all
        first-order and second-order risk sensitivities. This is the most
        comprehensive Greeks calculation endpoint.


        **Greeks Calculated:**

        - **Price**: Option theoretical value

        - **Delta**: Sensitivity to underlying price (∂V/∂S)

        - **Gamma**: Sensitivity of delta to underlying price (∂²V/∂S²)

        - **Vega**: Sensitivity to volatility (∂V/∂σ)

        - **Theta**: Sensitivity to time decay (∂V/∂t)

        - **Rho**: Sensitivity to interest rate (∂V/∂r)

        - **Vanna**: Cross-sensitivity to spot and volatility (∂²V/∂S∂σ)

        - **Volga**: Sensitivity of vega to volatility (∂²V/∂σ²)


        **Use Cases:**

        - Complete risk management analysis

        - Portfolio hedging calculations

        - Option trading strategy evaluation

        - Greeks-based position monitoring


        **Tier:** Standard (2 credits/request) [Tier: PRO, Credits: 5]
      operationId: bs_greeks_full
      requestBody:
        required: true
        content:
          application/json:
            schema:
              $ref: '#/components/schemas/BSPriceRequest'
            example:
              spot: 100
              strike: 105
              risk_free_rate: 0.05
              dividend_yield: 0.02
              volatility: 0.25
              time_to_maturity: 1
              option_type: call
      responses:
        '200':
          description: Successful calculation
          content:
            application/json:
              schema:
                type: object
                properties:
                  success:
                    type: boolean
                    example: true
                  data:
                    type: object
                    properties:
                      price:
                        type: number
                        example: 7.853
                      delta:
                        type: number
                        description: First derivative with respect to spot
                        example: 0.5234
                      gamma:
                        type: number
                        description: Second derivative with respect to spot
                        example: 0.0156
                      vega:
                        type: number
                        description: Sensitivity to 1% change in volatility
                        example: 32.862
                      theta:
                        type: number
                        description: Time decay per day
                        example: -0.0123
                      rho:
                        type: number
                        description: Sensitivity to 1% change in interest rate
                        example: 42.156
                      vanna:
                        type: number
                        description: 'Cross-sensitivity: spot and volatility'
                        example: -0.245
                      volga:
                        type: number
                        description: Vega sensitivity to volatility
                        example: 82.156
        '401':
          $ref: '#/components/responses/UnauthorizedError'
        '402':
          $ref: '#/components/responses/InsufficientCreditsError'
        '422':
          $ref: '#/components/responses/ValidationError'
components:
  schemas:
    BSPriceRequest:
      type: object
      required:
        - spot
        - strike
        - risk_free_rate
        - volatility
        - time_to_maturity
      properties:
        spot:
          type: number
          description: Current price of the underlying asset
          example: 100
        strike:
          type: number
          description: Strike price of the option
          example: 105
        risk_free_rate:
          type: number
          description: Risk-free interest rate (annualized, decimal format)
          example: 0.05
        dividend_yield:
          type: number
          description: Continuous dividend yield (annualized, decimal format)
          example: 0.02
          default: 0
        volatility:
          type: number
          description: Annualized volatility (decimal format)
          example: 0.25
        time_to_maturity:
          type: number
          description: Time to expiration in years
          example: 1
        option_type:
          type: string
          enum:
            - call
            - put
          description: Type of option
          example: call
          default: call
  responses:
    UnauthorizedError:
      description: Authentication information is missing or invalid
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: Invalid API key
    InsufficientCreditsError:
      description: Insufficient API credits for this request
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: string
                example: >-
                  Insufficient credits. This endpoint costs 2 credits per
                  request.
    ValidationError:
      description: Request validation failed
      content:
        application/json:
          schema:
            type: object
            properties:
              detail:
                type: array
                items:
                  type: object
                  properties:
                    loc:
                      type: array
                      items:
                        type: string
                    msg:
                      type: string
                    type:
                      type: string
  securitySchemes:
    APIKeyHeader:
      type: apiKey
      in: header
      name: X-API-Key
      description: >-
        API key for authentication. Get your key at
        https://api.fincept.in/auth/register

````